Matrix Converter Control Method and System

ABSTRACT

There is provided a method of generating a control strategy based on at least three switching states of a matrix converter. The at least three switching states are selected based on at least a predicted output current, associated with each switching state, and a desired output current. In particular, mathematical transformations of a desired output current as well as output currents associated with each of a plurality of switching states are used to identify appropriate switching states.

CROSS REFERENCE

This application is a U.S. National Phase of PCT InternationalApplication No. PCT/162017/056588, filed Oct. 24, 2017 and published asWO 2018/104808 on Jun. 14, 2018, which claims priority to Great BritainApplication No. GB1620647.6, filed Dec. 5, 2016. The entire disclosureof each of the above-identified applications is hereby incorporated byreference.

FIELD OF THE INVENTION

This invention relates to the field of matrix converters and morespecifically to the field of control methods for matrix converters.

BACKGROUND OF THE INVENTION

A matrix converter is typically a single stage AC-AC converter that usesan array of switches to convert a first AC signal (of any number ofphases) to a second AC signal (of any number of phases) with arbitrarymagnitude and frequency. One advantage of a matrix converter is that itdoes not need any large energy storage elements.

Typical matrix converters require each switch in the array of switchesto be a bidirectional switch capable of blocking voltage and conductingcurrent in both directions. A two-diode two-transistor bidirectionalswitch is a known method of independently controlling the direction ofthe current within a matrix converter.

One known modulation technique for a matrix converter uses Space VectorModulation (SVM) to perform modulation of the first AC signal. SeveralSVM techniques are known to those skilled in the art, such asthree-zero, two-zero and one-zero methods.

An example of a matrix converter and an SVM technique may be understoodwith reference to EP 1311057 A1.

SUMMARY OF THE INVENTION

The invention is defined by the claims.

According to an embodiment, there is provided a method of generating acontrol strategy for a multi-phase output matrix convertor, the matrixconverter being operable in a plurality of switching states, the methodcomprising: obtaining a target output transformation result representinga mathematical transformation result of a desired multi-phase outputcurrent of the matrix converter; identifying a plurality of switchingstates of the matrix converter; obtaining, for each switching state inthe identified plurality of switching states, a predicted outputtransformation result representing a mathematical transformation resultof a predicted output current for the switching state; identifying fromthe plurality of switching states at least three switching states,wherein, when mapped using a Cartesian co-ordinate system, a position ofthe target output transformation result is contained by an area definedby the positions of the predicted output transformation resultsassociated with the at least three switching states; and generating acontrol strategy for the matrix converter based on the at least threeswitching states.

Embodiments thereby provide a method of generating a control strategyfor a matrix converter based on predicted output currents of the matrixconverter. Possible switching states of the matrix converter are eachassociated with a respective switching state, where each switching statemay be associated with a respective predicted multi-phase outputcurrent. Mathematical transformations (e.g. an alpha-betatransformation) of both a desired multi-phase output current and thesepredicted output currents are used to identify which predicted outputcurrents, and thereby switching states, are to be used in the controlstrategy.

In particular, at least three of the switching states are identified forwhich the mathematical transformations of the three switching statesdefine an area which contains the mathematical transformation of thedesired output current.

Thus, a method according to an embodiment selects which switching statesare to be used in a control strategy based on at least a mathematicaltransformation of a predicted output current associated with eachswitching state, and a mathematical transformation of a desired outputcurrent of the matrix converter.

Embodiments allow for an enhanced control over the output current of amatrix converter, with a high degree of fidelity and reliability. Use ofpredicted output currents for determining switching states used in thecontrol strategy enables a fast and accurate determination of controlstrategy to be maintained.

The obtaining, for each switching state in the identified plurality ofswitching states, a predicted output transformation result may comprise:obtaining, for each switching state, a predicted output transformationresult from a simulated or mathematical model of the matrix converterand a load of the matrix converter.

Thus embodiments may comprise consulting or otherwise determining from asimulated or mathematical model of the matrix converter (and associatedload) the predicted output currents associated with one or moreswitching states. In embodiments, the simulated or mathematical modelmay be a table or dataset comprising a predicted output current (or morepreferably, mathematical transformations of the predicted outputcurrent) for each switching state for a variety of different possibleloads and/or input currents. Other simulated or mathematical models willbe apparent to the skilled person, such as a circuit simulation softwarepackage.

The obtaining, for each switching state in the identified plurality ofswitching states, a predicted output transformation result optionallycomprises: predicting, using a simulated or mathematical model of thematrix converter and a load of the matrix converter, an output currentof the matrix converter associated with each switching state in theidentified plurality of switching states; and performing a mathematicaltransformation on the predicted output current associated with eachswitching state to thereby obtain a predicted output transformationresult for each switching state in the identified plurality of switchingstates.

The identifying the at least three switching states may comprise:obtaining, for each switching state in the identified plurality ofswitching states, a predicted output transformation result errorrepresenting a predicted error between the predicted outputtransformation result associated with the switching state and the targetoutput transformation result; and identifying at least three switchingstates, wherein, when mapped using a Cartesian co-ordinate system, aposition of the origin is contained by an area defined by the positionsof the predicted output transformation result errors associated with theat least three switching states.

Thus there is proposed a method of generating a control strategy basedon a predicted error between a predicted output current by the matrixconverter and a desired/target output current. In particular, there maybe calculated, for each switching state/state of the matrix converter, apredicted error between a predicated output current by the matrixconverter operating in that switching state and a desired/target outputcurrent.

An improved reliability can be obtained by determining the at leastthree switching states based on a predicted error between the predictedoutput current(s) and the desired output current.

In at least one embodiment, the selection of which switching states areto be used to generate the control strategy may be narrowed down furtherbased on at least an input current associated with each switching stateand/or an output voltage associated with each switching state.

The identifying a plurality of switching states may comprise: obtaininga target input transformation result representing a mathematicaltransformation result of a desired input current of the matrixconverter; obtaining, for each possible switching state of the matrixconvertor, an input transformation result representing a mathematicaltransformation result of a current input of the matrix converterassociated with the possible switching state; identifying a plurality ofinput transformation results that are, when mapped using a Cartesianco-ordinate system, proximate to the position of the target inputtransformation result; and identifying the plurality of switching statesassociated with the identified plurality of input transformationresults.

Embodiments thereby recognise that the number of switching states forwhich a predicted output current need be calculated may be reduced basedon at least a desired input current.

Each switching state may be associated with a respective current input.Mathematical transformations of the current input of each switchingstate may be used to identify certain switching states further based on,for example, a mathematical transformation of the desired current input.

Thus, embodiments enable the control strategy to be generated furtherbased on a desired input current of the matrix converter.

The identifying the plurality of switching states may comprise:obtaining, for each possible switching state of the matrix convertor, asecond output transformation result representing a mathematicaltransformation result of a voltage output of the matrix converterassociated with the possible switching state; and identifying theplurality of switching states based on a magnitude of the second outputtransformation results.

Embodiments enable the number of switching states for which a predictedoutput current need to be calculated to be reduced based on at least amagnitude of an output voltage of the matrix converter. In particular,it is recognised that each switching state may be associated with arespective output voltage.

Mathematical transformations of the respective output voltages for eachswitching state may be used to further identify or narrow down whichswitching states are to be used for generating the control strategy.

Thus, embodiments enable to control strategy to be generated furtherbased on a voltage output of the matrix converter, and in particular, toa magnitude of voltage output by the matrix converter.

In at least one embodiment, the identifying the plurality of switchingstates based on a magnitude of the second output transformation resultscomprises identifying the plurality of switching states associated withthe second output transformation results of the largest magnitude.

The identifying the at least three switching states may comprise:identifying a first switching state for which a voltage differencebetween all output terminals of the matrix converter operating accordingto the first switching state is substantially zero; identifying a secondswitching state for which a voltage difference between at least twooutput terminals of the matrix converter operating according to thesecond switching state is non-zero; and identifying a third switchingstate for which a voltage difference between at least two outputterminals of the matrix converter operating according to the thirdswitching state is non-zero.

Thus, embodiments may comprise identifying at least one zero switchingstate and one non-zero or active switching state.

The generating the control strategy may comprise calculating a dutycycle for the at least three switching states based on the target outputtransformation result; and generating the control strategy for thematrix converter based on the calculated duty cycles.

Preferably, the mathematical transformation is an alpha-betatransformation, such that the target output transformation resultrepresents an alpha-beta transformation result of a desired multi-phaseoutput current of the matrix converter and each predicted outputtransformation result represents an alpha-beta transformation result ofa predicted output current for a respective switching state.

There is also proposed a computer program adapted to, when run on acomputer, perform a method as previously described.

According to another embodiment of the invention, there is provided amodulation strategy generator for a three-phase to three-phase matrixconvertor, the matrix converter being operable in a plurality ofswitching states, each switching state being associated with arespective switching state, the modulation strategy generator comprisinga processor which is adapted to: obtain a target output transformationresult representing a mathematical transformation result of a desiredoutput current of the matrix converter; identify a plurality ofswitching states of the matrix converter; obtain, for each switchingstate in the identified plurality of switching states, a predictedoutput transformation result representing a mathematical transformationresult of a predicted output current for the switching state; identifyfrom the plurality of switching states at least three switching states,wherein, when mapped using a Cartesian co-ordinate system, a position ofthe target output transformation result is contained by an area definedby the positions of the predicted output transformation resultsassociated with the at three switching states; and generate a modulationstrategy for the matrix converter based on at least three switchingstates.

The modulation strategy generator may be adapted to obtain, for eachswitching state, the predicted output transformation result from asimulated model of the matrix converter.

The modulation strategy generator may be adapted to predict, using asimulated model of the matrix converter, an output current of the matrixconverter associated with each switching state in the identifiedplurality of switching states; and perform a mathematical transformationon the predicted output current associated with each switching state tothereby obtain the predicted output transformation result for eachswitching state in the identified plurality of switching states.

The modulation strategy generator may be adapted to: obtain, for eachswitching state in the identified plurality of switching state, apredicted output transformation result error representing a predictederror between the predicted output transformation result associated withthe switching state and the target output transformation result; andidentify the at least three switching state, wherein, when mapped usinga Cartesian co-ordinate system, a position of the origin is contained byan area defined by the positions of the predicted output transformationresult errors associated with the at least three switching states.

BRIEF DESCRIPTION OF THE DRAWINGS

Examples of the invention will now be described in detail with referenceto the accompanying drawings, in which:

FIGS. 1A, 1B and 1C each illustrate a matrix converter;

FIG. 2 is a flowchart illustrating a method according to an embodiment;

FIGS. 3A and 3B illustrate mathematical transformations of predictedoutput currents for a plurality of switching states of the matrixconverter;

FIG. 4 illustrates predicted output current vectors for a plurality ofswitching states of the matrix converter;

FIG. 5 illustrates a control strategy according to an embodiment;

FIG. 6A illustrates mathematical transformations of current input for aplurality of switching states of the matrix converter.

FIGS. 6B-6C each illustrate mathematical transformations of voltageoutput for a plurality of switching states of the matrix converter;

FIG. 7 illustrates mathematical transformations of predicted outputcurrent errors for a plurality of switching states of the matrixconverter;

FIG. 8 illustrates a control strategy generator according to anembodiment;

FIGS. 9A and 9B illustrates mathematical transformations of predictedoutput current and current input respectively, for a plurality ofswitching state of the matrix converter;

FIG. 10 illustrates a system according to an embodiment;

FIGS. 11A and 11B illustrate experimental results of a system accordingto an embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

According to an embodiment of the invention, there is provided a methodof generating a control strategy based on at least three switchingstates of a matrix converter. The at least three switching states areselected based on at least a predicted output current, associated witheach switching state, and a desired output current. In particular,mathematical transformations of a desired output current as well asoutput currents associated with each of a plurality of switching statesare used to identify appropriate switching states.

Embodiments are at least partly based on the realisation that a controlstrategy that enables reliable and responsive control of a matrixconverter may be generated based on predicted output currents and adesired output current. Embodiments provide reliable methods ofidentifying suitable switching states of a matrix converter to be usedin generation of a control strategy.

Illustrative embodiments may, for example, be employed in electricaldrives or integrated drives which use a matrix converter. Otherimplementation strategies of such matrix converters will be readilyapparent to the skilled person.

FIGS. 1A, 1B and 10 each illustrate a matrix converter 10 adapted toconvert a three-phase input signal to a three-phase output signalaccording to different embodiments.

The matrix converter 5 comprises three input nodes 11 each connected toreceive a respective phase of an input signal from a three-phase ACpower supply 12. The matrix converter further comprises three outputnodes 13 each connected to provide a respective phase of an outputsignal to a load 14.

The voltage supply 12 may, for example, be a typical three-phase mainssupply or other three-phase AC power supply. The voltage supply 12 mayfor example, be modelled as three voltage or current sources, eachassociated with a different phase. Each voltage or current source may beprovided with an inductor and a damping resistor connected in parallel,each pair of inductor and damping resistor connecting a respectivevoltage or current source to a respective input node 11.

The load 14 may, for example, be a capacitive load or an inductive load,such that the matrix converter may comprise, as illustrated in FIG. 1A,a capacitive port 15 or, as illustrated in FIG. 1B, an inductive port 16or both.

Of course, it will be appreciated that in some embodiments, such as thatillustrated by FIG. 10, a matrix converter 1 need not comprise aspecific output port. Such embodiments may be used, for example, if theload 14 comprises an induction machine.

Each output node 13 is connectable to each input node 11 by a respectivebidirectional switch. The matrix converter 10 thereby comprises an arrayof nine (3×3) bidirectional switches.

A capacitor arrangement 18 may be provided, as illustrated in FIG. 1B,so as to provide a path for the inductive current of each phase. Such acapacitor arrangement may not be required, for example, if the matrixconverter comprises a capacitive port 15, such as that illustrated byFIG. 1A.

In order to prevent line-to-line short circuits (of the voltage source),no two bidirectional switches associated with a single output nodeshould be switched on at any given moment. Similarly, to ensure there isa path for the inductive current of each phase of the input signal, viathe capacitor arrangement 18 or the capacitive port 15, no output node13 should be disconnected from every input node 12. This prevents largeover-voltages from occurring. In other words, each output node 13 mustalways be connected to receive a phase of the voltage source 12. Thesetwo restrictions allow for improved device safety, reliability andlongevity.

As will be apparent to the skilled person, a matrix converter 10 isoperable in a finite number of switching states, each switching staterepresenting a different open-and-close configuration of thebidirectional switches. For the matrix converter 10 of FIG. 1, there areonly 27 switching states which comply with the above-identifiedrestrictions.

As used herein, a ‘zero switching state’ is defined to be a switchingstate in which the voltage between each output node and a referencevoltage is substantially the same. For example, each output node 13 maybe connected to a same input node 11. As such, there is no or negligiblevoltage difference between any of the output nodes 13 (as each outputnode is at the same voltage).

A ‘non-zero switching state’ or ‘active switching state’ is defined tobe a switching state in which the voltage difference between each of atleast two output nodes and a reference voltage is different. Forexample, two or more output nodes may be connected to different inputnodes. As such, there is a voltage difference between at least twooutput nodes.

A control strategy may be used to define which output node is connectedto which input node at any given time (i.e. which switching state amatrix converter operates in). Such a control strategy may enablemodulation of the voltage supply to the load. In particular, a pulsewidth modulation control strategy may be used to define how long amatrix vector is operated in a particular switching state.

A controller (not shown), such as a field-programmable gate array(FPGA), may use the control strategy to control the switching of thebidirectional switches. By way of example only, a controller may providea variable voltage connection to one or more transistors of eachbidirectional switches in order to control the conductivity of thetransistor(s), thereby enabling control of the bidirectional switch.

With further reference to FIGS. 2 to 4, there will be described a method2 of generating a control strategy for a multi-phase output matrixconverter 10 according to an embodiment.

For embodiments hereafter described, transformation results generallyrefer to results of an alpha-beta transformation of a multi-phasesignal. Of course, other results of mathematical transformations of amulti-phase signal may be used to various advantages, such as adirect-quadrature-zero transformation, also known as a dq0, dqo, 0dq orodq transformation. Generally speaking, a mathematical transformationchanges the reference frame of a particular multi-phase signal, andpreferably provides a two-dimensional or two-part result in an analogousmanner to a complex value. It will be understood by the skilled personthat such a result may be represented as a pair of numbers (e.g.co-ordinates), or by a corresponding vector.

FIG. 2 illustrates a flowchart of the method 2 for generating thecontrol strategy according to an embodiment.

FIGS. 3 and 4 each illustrate transformation results associated with adesired output current and predicted output currents of the matrixconverter, plotted using a Cartesian coordinate system in a mathematical(e.g. alpha-beta) plane.

The method comprises obtaining 20 a target output transformation result30 representing a mathematical (e.g. alpha-beta) transformation resultof a desired multi-phase output current of the matrix converter 10. Thetarget output transformation result 30, when considered as a vector fromthe origin, may be considered as a target output current vector.

The method further comprises identifying 22 a plurality of switchingstates associated with the matrix converter 10. This may comprise, forexample, identifying only a subset or selection of all availableswitching states of the matrix converter 10 for further processing. Inother examples, all switching states associated with the matrixconverter are identified for further processing.

Preferably, the identified plurality of switching states comprises atleast one zero switching state and two or more non-zero switchingstates. Even more preferably, the identified plurality of switchingstates comprises at least one zero switching state, and six or morenon-zero switching states.

The method further comprises obtaining 24, for each identified switchingstate, a predicted output transformation result 31, 32, 33, 34, 35, 36,37 representing a mathematical (e.g. alpha-beta) transformation resultof a predicted multi-phase output current for a matrix converter 10operating in accordance with the respective switching state. Eachpredicted output transformation result, when considered as a vector fromthe origin, may be considered as a predicted output current vectorassociated with a respective switching state.

Thus, FIGS. 3 and 4 may illustrate predicted output current vectors 31,32, 33, 34, 35, 36, 37 associated with predicted output currents of anidentified plurality of switching states, as well as a target outputcurrent vector 30 associated with a target/desired output current.

The alpha-beta transformation results of a predicted output current(i.e. the predicted output current vectors) may be obtained, forexample, from a model or simulation of the matrix converter and anassociated load, which may be a predicted load or a default load. Forexample, a model may comprise a dataset or table, or, in someembodiments, may comprise circuit simulation software. The outputcurrent may be considered to be the current provided to a load (i.e. aload current).

Equations (1) and (2) illustrate a predictive load model for a simple RLload (having resistance R and an inductance L). The equations make useof the switching period Ts (being the reciprocal of the switchingfrequency).

$\begin{matrix}{{I_{o}^{j}\left( {k + 1} \right)} = {{\left( {1 - \frac{{RT}_{s}}{L}} \right){I_{o}(k)}} + {\frac{T_{s}}{L}{V_{o}^{j}(k)}}}} & (1) \\{e_{j} = {{I_{o}^{j}\left( {k + 1} \right)} - {I_{o}(k)}}} & (2)\end{matrix}$

where l_(o)(k+1) and l_(o)(k) are the load currents at (k+1) and kinstants respectively for j={0, 1, 2 . . . } where j is the identifiedswitching state.

It has been recognised that different switching states are associatedwith different predicted output currents, which are respectivelyrepresented by the different output transformation results definingpredicted output current vectors.

As illustrated by FIGS. 3A and 3B, transformation results 31, 32, 33,34, 35, 36, 37 of the predicted output currents may form one or moreskewed polygons, here a single skewed hexagon with an offset centre.

The method 2 further comprises identifying 26 at least three switchingstates, for which the associated predicted output transformation results31, 32, 37 define an area 40 or region in which the target outputtransformation result 30 is located. Thus, switching states, associatedwith at least three predicted output current vectors 31, 32, 37 definingan area 40 containing the target output transformation result 30, may beidentified.

The method may therefore comprise identifying 26 at least threeswitching states which are used to generate the control strategy.

The identifying at least three switching states preferably comprisesidentifying at least one zero switching state (i.e. associated with azero switching state transformation result 37) and at least two non-zeroswitching states (i.e. associated with a first 31 and second 32 non-zeroswitching state transformation result).

Although zero switching states provide a same voltage between outputnodes of the matrix converter, an output current provided by a matrixconverter operating according to a zero switching state may be non-zero(e.g. due to properties of a load, such as inductance, resistance,impedance, back electromagnetic field effects and so on). This is bestillustrated by FIG. 3A, which identifies a mathematical transformation37 of a predicted output current associated with a zero switching stateas non-zero.

In particular, as illustrated in FIG. 3B, an area containing the targetoutput transformation result may be defined in the following way. Apredicted output transformation result 37 associated with a particularzero switching state (i.e. a zero switching state transformation result37) may define a centre of circle of infinite diameter. The method maycomprise identifying a first non-zero vector (associated with a firstnon-zero switching state transformation result 31) and a second non-zerovector (associated with a second non-zero switching state transformationresult 32) for which a sector of this circle, when bounded on one sideby a line beginning at the zero switching state transformation result 37and intersecting the first non-zero switching state transformationresult 31 and on the other side by a line beginning at the zeroswitching state transformation result 37 and intersecting the secondnon-zero switching state transformation result 32, defines an area inwhich the target output transformation result 30 is positioned.

By way of another example, the predicted output transformation results31, 32, 37 of the identified at least three switching states may definevertices of an area, such as a triangle, which contains the targetoutput transformation result 30.

By way of yet another example, the identifying the at least threeswitching states may comprise identifying the three predicted outputtransformation results 31, 32, 37 most proximate to the target outputtransformation result 30, and identifying the associated switchingstates.

In this way, the method 2 selects which switching states are to be usedin the generation of the control strategy based on at least mathematicaltransformations of a predicted output current of the matrix converterfor different switching states and a mathematical transformation of adesired output current of the matrix converter.

The method 2 further comprises generating 28 a control strategy for theplurality of identified switching states. The generating 28 may comprisedetermining appropriate duty cycles for each switching state in theplurality of identified switching states and generating a control schemebased on the identified duty cycles.

With further reference now to FIG. 4, and as briefly described earlier,each transformation result 31, 32, 37 may be considered to be apredicted output current vector associated with a respective switchingstate or switching state.

By way of example, a first non-zero switching state transformationresult 31 may be associated with a first predicted current vector 51,{right arrow over (ι_(o1))}, a second non-zero switching statetransformation result 32 may be associated with a second predictedcurrent vector 52, {right arrow over (ι_(o2))}, and the zero switchingstate transformation result 37 may be associated with a zeroth predictedcurrent vector 57, {right arrow over (ι_(o0))}. Similarly, the targetoutput transformation result 30 may be associated with a target currentvector 50, {right arrow over (ι_(ot))}.

The generating a control strategy may comprise identifying the linearcombination of the first 51 and second 52 predicted current vectors andthe zeroth predicted current vector which results in the target currentvector 50. The calculated duty cycle for each predicted current vectoris assigned as the duty cycle of its associated switching state.

In particular, the appropriate linear combination may be calculated byconsidering the following equations.

{right arrow over (ι_(o1))}·d ₁+{right arrow over (ι_(o2))}·d ₂+{rightarrow over (ι_(o0))}·d ₀={right arrow over (ι_(ot))}  (3)

d ₁ +d ₂ +d ₀=1  (4)

Where {right arrow over (ι_(o1))} represents the first predicted currentvector, {right arrow over (ι_(o2))} represents the second predictedcurrent vector, {right arrow over (ι_(o0))} represents the zerothpredicted current vector, {right arrow over (ι_(ot))} represents thetarget current vector, d₁ represents the duty cycle of the firstpredicted current vector, d₂ represents the duty cycle of the secondpredicted current vector and d₀ represents the duty cycle of the zerothpredicted current vector.

The resultant vectors {right arrow over (ι_(o1))}·d₁, {right arrow over(ι_(o1))}·d₂ and {right arrow over (ι_(o1))}·d₀ are illustrated in FIG.4 for the purposes of clarity. As will be apparent, the combination ofthese three resultant vectors results in the target current vector 50.

In this way, duty cycles (i.e. relative operation time) for eachpredicted current vector which results in the appropriate target vectormay be calculated. A control strategy for the plurality of identifiedswitching states may be calculated based on the determined duty cycles.

For example, with reference to FIG. 5, generating the control strategymay comprise generating a double sided switching pattern for the matrixcontroller based on the calculated duty cycles for the predicted currentvectors.

A zero switching state v₀ associated with the zeroth predicted currentvector {right arrow over (ι_(o0))} may have its calculated duty cycle d₀divided into three portions, two of an equal size and one twice the sizeof the others. A first non-zero switching state v₁ associated with thefirst predicted current error {right arrow over (ι_(o1))} may have itscalculated duty cycle d₁ evenly divided into two portions. Similarly, asecond non-zero switching state v₁ associated with the second predictedcurrent error {right arrow over (ι_(o2))} may have its calculated dutycycle d₂ evenly divided into two portions.

The divided portions of the duty cycles may be arranged in a pattern asillustrated in FIG. 5.

Proposed embodiments enable fast dynamic response without compromisingon the quality of output signals or waveforms by the matrix converter.

Proposed methods may be used to predict the output voltage with improvedaccuracy since the dynamics of an input filter mean that the outputvoltage generated by other control strategies such as SVM may beinaccurate.

In some embodiments, the predicted current vector may be a predictedinput current vector, so as to enable control over the input current tothe matrix converter.

A more detailed embodiment of generating a control strategy will bedescribed with reference to FIGS. 6A to 7.

In embodiments, the identifying a plurality of switching states of thematrix converter may comprise iteratively limiting or narrowing down aselection of switching states to identify only a portion of allavailable switching states. A number of possible methods may be used tonarrow down or limit this selection.

As previously mentioned, for the matrix converter 10 of FIG. 1, thereare only 27 switching states which comply with certain restrictions. Ofthese, six are considered rotating or synchronous switching states thatonly provide changes in magnitude and direction between the input nodesand the output nodes. For the sake of simplicity, in at least oneembodiment, there is no need to consider these switching states. Theremaining vectors/switching states may be referred to as: 0 (i.e. zeroswitching states), ±1, ±2, ±3, ±4, ±5, ±6, ±7, ±8, and ±9. It is notedthat there are three zero switching states.

The present invention recognises that the number of switching states maybe further or otherwise narrowed down by limiting to switching stateswhich meet particular criteria for input/output signals.

By way of example, the number of switching states may be narrowed downbased on a multi-phase input current of the matrix converter and/or amulti-phase output voltage of the matrix converter.

A matrix converter 10 operating in accordance with a particularswitching state may be associated with a respective input currentvector, which is representative of an input current of the matrixconverter operating in the particular switching state.

Similarly, a matrix converter 10 operating in accordance with aparticular switching state may be associated with a respective outputvoltage vector, which is representative of an output voltage of thematrix converter operating in the particular switching state.

That is, each switching state is associated with a respective inputcurrent vector and an output voltage vector, as illustrated in FIGS. 6Aand 6B.

FIG. 6A illustrates input current vectors for a matrix converter 10,each being a mathematical (e.g. alpha-beta) transformation result of aninput current of the matrix converter 10 associated with a respectiveswitching state.

FIG. 6B illustrates output voltage vectors for a matrix converter 10,each being a mathematical (e.g. alpha-beta) transformation result of avoltage output by the matrix converter 10 for each respective switchingstate.

The selection of switching states may be limited to only those switchingstates for which the associated input current vector is proximate to adesired input current vector. Thus, a desired input current, associatedwith a desired input current vector, may define which switching statesare selected.

The selection of switching states may be based on a magnitude of theassociated output voltage vectors.

For example, in some embodiments only switching states having an outputvoltage vector of the greatest magnitude (e.g. the outermost outputvoltage vectors of FIG. 6B) may be selected. This may ensure a maximumpower output of the matrix converter.

In other examples, only the switching states having an output voltagevector of the lowest magnitude may be selected. This may ensure anincreased control over the input current angle.

More than one method of limiting which switching states are identifiedmay be used to particular advantage.

In one scenario, with reference to FIG. 6A, a desired input currenttransformation result lies within a first sector 61. Switching statesthat can produce an input current in that sector are ±3, ±6, ±9, ±1, ±4and ±7. The plurality of switching states is firstly limited to theseidentified switching states, i.e. an initial set of 12 switching states.

FIG. 6C illustrates the output voltage vectors for the above scenario inwhich the selection of switching states has been initially narrowed downto select only the switching states ±3, ±6, ±9, ±1, ±4 and ±7, eachbeing associated with an input current that may provide the desiredinput current. The distribution of the output voltage vectors for eachof these switching states is illustrated in FIG. 6C.

In an embodiment, only those switching states which are associated withthe output voltage vectors with greatest magnitude are selected (i.e.those voltage vectors lying in the outer hexagon of FIG. 6C).

Thus, by way of example, the switching states ±4, ±7 and ±1 may beselected as the identified plurality of switching vectors for furtherprocessing.

Embodiments recognise that a switching state of a matrix converter maybe associated with a plurality of vectors representing differentparameters of the matrix converter. As described previously, a switchingstate may be associated with: a predicted output current vector(representing a predicted multi-phase output current of a matrixconverter operating according to the switching state); a input currentvector (representing a multi-phase current input to the matrix converteroperating according to the switching state) and a voltage outputswitching vector (representing a multi-phase voltage output by thematrix converter operating according to the switching state).

Embodiments also recognise that the identification of switching statesfor which a control strategy is generated may be based on(characteristics of) a plurality of vectors associated with eachswitching state.

According to a preferred embodiment, obtaining a predicted outputtransformation result (i.e. a predicted current vector) for eachidentified switching state comprises obtaining a predicted current errorvector for each identified switching state.

A predicted current error vector may be represented by the mathematical(e.g. alpha-beta) transformation result of a predicted error between anoutput current of the matrix converter for an associated switching stateand a desired output current. Thus, an error between a predicted outputcurrent and a desired output current may be calculated for each relevantswitching state. A mathematical transformation of this error mayrepresent the predicted current error vector of that switching state.

In other or further embodiments, a predicted current error vector of aswitching state may be modelled as a difference between a transformationresult of a predicted output current associated with the switching stateand a transformation result of a desired output current.

Thus, there may be considered a predicted output transformation resulterror which represents a predicted error between the predicted outputtransformation result associated with the switching state and the targetoutput transformation result.

FIG. 7 illustrates the predicted current error vectors e₁, e₂, e₃, e₄,e₅, e₆, for a plurality of identified switching states. Thus, FIG. 7illustrates transformation results associated with predicted multi-phaseoutput current errors of the matrix converter for different switchingstates, plotted using a Cartesian coordinate system in a mathematical(e.g. alpha-beta) plane.

According to an embodiment, there is an objective to minimize or obtainzero output current error. The target is therefore the origin of theplane (0,0). It may thereby be understood that the ‘target outputtransformation result’, as described with reference to FIG. 2-5, ispresently embodied as the origin of the plane. That is, the targetoutput transformation result may be a point positioned at (0,0).

The predicted current error vectors illustrated in FIG. 7 include atleast one zero switching state predicted current error vector e₀ (beingthe predicted current error vector associated with a zero switchingstate) and a plurality of non-zero switching state predicted currenterror vectors, each associated with a respective non-zero switchingstate. The other predicted current error vectors include at least afirst predicted current error vector e₁, a second predicted currenterror vector e₂, as well as third e₃, fourth e₄, fifth e₅, and sixth e₆predicted current error vectors.

The control problem is to find the linear combination of at least threepredicted current error vectors which will result in zero current error(i.e. targeting the origin). This may be obtained by a linearcombination of the zero switching state predicted current error vectorand non-zero switching state predicted current error vectors.

In particular, a solution exists if the target (origin) lies within anarea formed the zero switching state predicted current error vector andat least two non-zero switching state predicted current error vectors.If the target (origin) lies outside this area, it is considered as theover-modulation condition, and different measures, described later, needto be taken to address it.

In particular embodiments, it may be determined that the solution existsif the target lies within an area defined by the zero switching statepredicted current error vector and two adjacent non-zero switching statepredicted current error vectors. A first non-zero switching statepredicted current error vector e₁ may be considered to be adjacent to asecond non-zero switching state predicted current error vector e₂ if thesecond non-zero switching state predicted current error vector e₂ is oneof the two most proximate non-zero switching state predicted currenterror vectors to the first non-zero switching state predicted currenterror vector e₁.

For each pair of adjacent non-zero switching state predicted currenterror vectors, a solution exists if the following conditions are met:

(e _(x) −e ₀)×(−e ₀)·(e _(y) −e ₀)×(−e ₀)≤0  (5)

(e _(x) −e ₀)·(−e ₀)>0  (6)

(e _(y) −e ₀)·(−e ₀)>0  (7)

where e_(x) is one of the non-zero vector predicted current errorvector, and e_(y) is an adjacent non-zero vector predicted current errorvector.

The solution for the embodiment illustrated by FIG. 7 is e_(x)=e₁ ande_(y)=e₂.

The adjacent pair of non-zero vector predicted current error vectorsthat meet these requirements are selected (i.e. used as e_(x) ande_(y)), together with the zero switching state predicted current errorvector e₀, in order to generate a control strategy.

The linear combination of these vectors to obtain the target (i.e. theorigin) can then be obtained by solving the following set of linearequations

(e _(xα) −e _(oα))·d ₁+(e _(yα) −e _(0α))·d ₂ =−e _(0α)  (8)

(e _(xβ) −e _(0β))·d ₁+(e _(yβ) −e _(0β))·d ₂ =−e _(0β)  (9)

d ₁ +d ₂ +d ₀=1  (10)

where d₁ and d₂ are the respective duty cycles for the adjacent pair ofnon-zero switching state predicted current error vectors that meet theconditions of equations (5)-(7), and d₀ is the duty cycle for the zeroswitching state predicted current error vector.

However, if d₁+d₂>1, this implies that the target point (the origin)lies outside the hexagon formed by area bordered by the non-zeroswitching state predicted current error vectors e₁, e₂, e₃, e₄, e₅, e₆(i.e. the other predicted current error vectors). In this case, anattempt to reach the target point (the origin) is achieved by modulatingbetween the adjacent pair of non-zero vector predicted current errorvectors e_(x), e_(y). That is, the method comprises identifying a dutycycle for the adjacent pair of non-zero vector predicted current errorvectors that meet these requirements of equations (5)-(7) that resultsin a resultant vector closest to the origin.

Generating a strategy on this basis generates accurate duty cyclesdepending upon the error predictions, and results in fixed switchingfrequency operation. Due to at least the fact that the control strategyis generated on a predicted output current, the control strategy willhave fast transients.

Proposed control methods provide a fast dynamic response, e.g. to achange in desired or target output current of the matrix converter, withlittle compromise of the quality of the controlled waveforms or outputsignals.

Moreover, the steady state performance may be improved due to themodulation approach included in the method. Thus, a combination ofpredictive control and appropriate modulation described herein resultsin a good steady state performance with a fast dynamic response.

This embodiment is considered to be a method of direct predictivecurrent-error vector control (DPCVC). There is proposed a concept ofconsidering the current error in its vector form in a transformed plane(such as the αβ plane) as a cost function in order to calculate the dutycycles or application times for the converter switching states. Theobjective is to minimize the load current error, making it equal to zeroif possible. Therefore, the target point to achieve when the loadcurrent errors are plotted is the origin of the plane.

FIG. 8 illustrates a control strategy generator 8 according to anembodiment. The control strategy generator 8 is adapted to generate acontrol strategy 87 a for a matrix converter controller 88 adapted tocontrol a matrix converter 89.

The control strategy generator 8 comprises a switching state provisionunit 81 adapted to provide information about switching states associatedwith the matrix converter 89. For example, the switching state provisionunit 81 may indicate all available switching states of the matrixconverter, or may indicate only non-rotating switching states of thematrix converter.

The control strategy generator 8 further comprises a switching stateidentification unit 82, which is adapted to identify a plurality ofswitching states of the matrix converter. By way of example, theswitching state identification unit may identify a plurality ofswitching states based on a desired input current of the matrixconverter or based on a magnitude of output voltage vectors associatedwith the switching states, as previously described with reference toFIGS. 6A-6C.

The control strategy generator 8 further comprises a circuit simulator83, which is adapted to simulate an operation of the matrix converter89. In particular, the circuit simulator 83 comprises models of an ACsource 83 a (which models an AC source of the matrix converter 89), aninput filter 83 b, a matrix converter 83 c (which models the matrixconverter 89) and a load 83 d (which models a load of the matrixconverter 89). A predicted multi-phase load current (i.e. outputcurrent) i_(o) is output by the circuit simulator.

Each of the plurality of switching states identified by the switchingstate identification unit is simulated by the circuit simulator. Thus,the model of the matrix converter 83 c is controlled according to eachof the identified plurality of switching states.

The simulated multi-phase output current i_(o) is provided to amathematical transformation unit 84 of the control strategy generator.The mathematical transformation unit 84 mathematically transforms (e.g.using an alpha-beta transformation) the simulated multi-phase currenti_(o) to obtain, for each switching state in the identified plurality ofswitching states, a predicted output transformation result representinga mathematical transformation result of a predicted output current forthe switching state.

Furthermore, the mathematical transformation unit 84 may also obtain atarget output transformation result representing a mathematicaltransformation result of a desired multi-phase output current of thematrix converter. This may be done, for example, by performing amathematical transformation, such as an alpha-beta transformation, on adesired input current i_(o).

A switching state selection unit 85 identifies from the plurality ofswitching states at least three switching states, wherein, when mappedusing a Cartesian co-ordinate system, a position of the target outputtransformation result is contained by an area defined by the positionsof the predicted output transformation results associated with the atleast three switching states. Thus the switching state selection unitidentifies at least three switching states based on the predicted outputtransformation results and a target output transformation result.

A duty cycle generator 86 determines a duty cycle for each at leastthree switching states, for example, employing a method previouslydescribed.

A control strategy generator 87 generates a control strategy for thematrix converter 89 based on at least the determined duty cycles foreach at least three switching states, for example, employing methodspreviously described. In embodiments, the control strategy generator 87arranges the at least three switching states into a control patternbased on their determined duty cycles.

In some embodiments, the mathematical transformation unit 84 obtains amathematical transformation of a predicted output current error based ona predicted output current i_(o) by the circuit simulator and a desiredoutput current 84 a.

Of course, it will be appreciated that in some embodiments, the circuitsimulator 83 generates a predicted output current error associated witheach switching state, for example based on the desired output current 84a, such that the mathematical transformation unit 84 performs amathematical transformation of predicted output current errors.

In embodiments, the simulated or mathematical model (e.g. the circuitsimulator 83) may be a table or dataset which identifies a predictedoutput current (or more preferably, a predicted output current error)for each switching state for a variety of different possible loadsand/or input currents. Other simulated or mathematical models will beapparent to the skilled person, such as a circuit simulation softwarepackage.

Methods according to at least one embodiment may be repeatediteratively, as the predicted output current by the matrix converter maydynamically change dependent upon, for example, changes to the load or acurrent operation of the matrix converter. A load may react or responddifferently for a matrix converter operating in different switchingstates, which may influence the prediction of the output current foridentified switching states.

Particularly advantageous embodiments may include continually attemptingto reduce an error of the output current by iteratively determiningpredicted output current errors associated with identified switchingstates, and determining a control strategy based on the predicted outputcurrent errors, as previously described.

Predicted output currents may be determined based on information about apresent switching state of the matrix converter and a present outputcurrent. Thus, information about the present or ongoing operation of thematrix converter may be used to predict likely output currents of thematrix converter for different possible switching states. By way ofexample, information about a present output current may provideinformation about characteristics of a load of the matrix converter,which may be used to improve a simulation of the load.

Thus a control strategy may be automatically adjusted and changed over aperiod of time.

According to at least one other embodiment, there is proposed a methodof generating a control strategy that enables control over an inputcurrent and an output current of the matrix converter.

In particular, a method according to an embodiment may compriseidentifying at least five switching states which are used to generatethe control strategy.

In a similar manner to methods previously described, identifying atleast five switching states may comprise iteratively selectingparticular switching states from all possible switching states based ona predicted output current, desired input current and/or a magnitude ofoutput voltage vectors associated with switching states.

Preferably, identifying the at least five switching states comprisesidentifying at least three switching states according to a methoddescribed with reference to at least FIGS. 2 to 7. In particular, theidentified at least three switching states may comprise a zero switchingstate and at least two non-zero switching states.

For the purposes of the hereafter described embodiment, the threeidentified switching states may comprise a zero switching state, a firstnon-zero switching state and a second non-zero switching state.

As before, each switching state may be associated with a transformationresult of a predicted output current error, which corresponds to apredicted output current error vector. Thus, as illustrated in FIG. 9A,a zero switching state is associated with a zeroth predicted outputcurrent error vector e₉₀, a first non-zero switching state is associatedwith a first predicted output current error vector e₉₁ and a secondnon-zero switching state is associated with a second predicted outputcurrent error vector e₉₂.

The method further comprises identifying at least two further switchingstates, being a third non-zero switching state and a fourth non-zeroswitching state. A third predicted output current error vector e₉₃associated with the third non-zero switching state lies substantially ona line intersecting the zeroth predicted output current error vector e₉₀and the first predicted output current error vector e₉₁. A fourthpredicted output current error vector e₉₄ associated with the fourthnon-zero switching state lies substantially on a line intersecting thezeroth predicted output current error vector e₉₀ and the secondpredicted output current error vector e₉₂.

In this way, and as illustrated in FIG. 9B, phase angles of inputcurrent vectors associated with the first i_(i_1) and second i_(i_2)non-zero vectors are the same, and phase angles of input current vectorsassociated with the third i_(i_3) and fourth i_(i_4) non-zero vectorsare the same. However, a magnitude of the first and third non-zero inputcurrent vectors may be different, as may a magnitude of the second andfourth non-zero input current vectors.

Once the five switching states have been identified, comprising fournon-zero switching states and a zero switching state, a control strategyfor the matrix converter may be generated. There is an aim of achievingcontrol of the input current angle as well as maintain zero outputcurrent error. It is assumed that the desired input current is in phasewith voltage supplied to the matrix converter (i.e. from a voltagesupply).

With particular reference to FIG. 9B, the selected four non-zeroswitching states are each associated with a respective input currentvector, which represent a transformation result. Thus, a first non-zeroswitching state is associated with a first input current vector i_(i_1),a second non-zero switching state is associated with a second inputcurrent vector i_(i_2) a third non-zero switching state is associatedwith a third input current vector i_(i_3) and a fourth non-zeroswitching state is associated with a fourth input current vectori_(i_4). An input current associated with the zero switching state is 0,such that an input current vector of the zero switching state is a zerovector located at the origin.

A reference input current vector i_(i_ref) may be obtained from thevoltage supply, having a reference input current vector angle b_(i). Forexample, the reference input current vector may be obtained from amulti-phase voltage output by the voltage (as it may be assumed that thevoltage output of the voltage supply should be synchronised with theinput current to the matrix converter).

A linear combination of the identified five switching states may beidentified to meet both output current vector requirements and inputcurrent vector requirements by solving the following set of linearequations:

(e _(91∝) −e _(90α))·d ₁+(e _(92∝) −e _(90α))·d ₂+(e _(93∝) −e _(90α))·d₃+(e _(94∝) −e _(90α))·d ₄ =−e _(90α)  (11)

(e _(91β) −e _(90β))·d ₁+(e _(92β) −e _(90β))·d ₂+(e _(93β) −e _(90β))·d₃+(e _(94β) −e _(90β))·d ₄ =−e _(90β)  (12)

(−i _(i_1∝) sin(bi)+i _(i_1β) cos(bi))·d ₁+(−i _(i_3∝) sin(bi)+i _(i_3β)cos(bi))·d ₃=0  (13)

(−i _(i_2∝) sin(bi)+i _(i_2β) cos(bi))·d ₂+(−i _(i_4∝) sin(bi)+i _(i_4β)cos(bi))·d ₄=0  (14)

d ₁ +d ₂ +d ₃ +d ₄ +d ₀=0  (15)

and d₁, d₂, d₃, d₄ are the duty cycles for each respective non-zeroswitching state and d₀ is the duty cycle for the zero switching state.

At least one embodiment provides a method of generating a controlstrategy, which uses multiple switching states, based on a singleanalysis of a desired output current. Such a control strategy provides afast response to a change in demanded output current with a high degreeof accuracy and low total harmonic distortion. The control strategy maybe iteratively generated to repeatedly ensure a suitable current isoutput.

The control strategies described herein enable a fixed or predictableswitching frequency of the matrix converter to be provided, whichincreases an ease in the design of an input filter.

Although above described embodiments relate to a three-phase tothree-phase matrix converters, it will be understood that matrixconverters according to other embodiments of the invention may beconnected to an input supply of an arbitrary number of phases, such as atwo-phase supply or a four-phase supply. Conceivably, embodiments may beapplied to matrix converters adapted to output a converted supply of anarbitrary number of phases, such as two-phase, four-phase or five-phaseoutputs.

Proposed embodiments enable modification of the method (e.g. atsaturation or an over-modulation condition) to prioritize control ofinput and/or output currents. In particular, the method may be modifiedto prioritize control of input currents (i.e. rather than outputcurrents), depending on the requirements. This may be performed byobtaining predicted input currents and appropriate transformationresults thereof.

In some embodiments, there may be provided a system comprising aprocessing arrangement adapted to carry out any method previouslydescribed with reference to FIG. 1 to 7, 9A or 9B.

By way of example, as illustrated in FIG. 10, embodiments may comprise acomputer system 100. The components of computer system/server 101 mayinclude, but are not limited to, one or more processing arrangements,for example comprising processors or processing units 101, a systemmemory 104, and a bus 108 that couples various system componentsincluding system memory 104 to processing unit 101.

Bus 108 represents one or more of any of several types of busstructures, including a memory bus or memory controller, a peripheralbus, an accelerated graphics port, and a processor or local bus usingany of a variety of bus architectures. By way of example, and notlimitation, such architectures include Industry Standard Architecture(ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA)bus, Video Electronics Standards Association (VESA) local bus, andPeripheral Component Interconnect (PCI) bus.

Computer system/server 100 typically includes a variety of computersystem readable media. Such media may be any available media that isaccessible by computer system/server 100, and it includes both volatileand non-volatile media, removable and non-removable media.

System memory 104 can include computer system readable media in the formof volatile memory, such as random access memory (RAM) 105 a and/orcache memory 105 b. Computer system/server 100 may further include otherremovable/non-removable, volatile/non-volatile computer system storagemedia. By way of example only, storage system 104 can be provided forreading from and writing to a non-removable, non-volatile magnetic media(not shown and typically called a “hard drive”). Although not shown, amagnetic disk drive for reading from and writing to a removable,non-volatile magnetic disk (e.g., a “floppy disk”), and an optical diskdrive for reading from or writing to a removable, non-volatile opticaldisk such as a CD-ROM, DVD-ROM or other optical media can be provided.In such instances, each can be connected to bus 90 by one or more datamedia interfaces. As will be further depicted and described below,memory 104 may include at least one program product having a set (e.g.,at least one) of program modules that are configured to carry out thefunctions of embodiments of the invention.

Program/utility 107 a, having a set (at least one) of program modules107 b, may be stored in memory 104 by way of example, and notlimitation, as well as an operating system, one or more applicationprograms, other program modules, and program data. Each of the operatingsystem, one or more application programs, other program modules, andprogram data or some combination thereof, may include an implementationof a networking environment. Program modules 108 b generally carry outthe functions and/or methodologies of embodiments of the invention asdescribed herein.

Computer system/server 100 may also communicate with one or moreexternal devices 109 a such as a keyboard, a pointing device, a display109 b, etc.; one or more devices that enable a user to interact withcomputer system/server 100; and/or any devices (e.g., network card,modem, etc.) that enable computer system/server 100 to communicate withone or more other computing devices. Such communication can occur viaInput/Output (I/O) interfaces 102. Still yet, computer system/server 100can communicate with one or more networks such as a local area network(LAN), a general wide area network (WAN), and/or a public network (e.g.,the Internet) via network adapter 103. As depicted, network adapter 103communicates with the other components of computer system/server 100 viabus 108. It should be understood that although not shown, other hardwareand/or software components could be used in conjunction with computersystem/server 100. Examples, include, but are not limited to: microcode,device drivers, redundant processing units, external disk drive arrays,RAID systems, tape drives, and data archival storage systems, etc.

FIGS. 11A and 11B illustrate experimental results of a system having athree-phase output matrix converter, wherein the matrix converter iscontrolled by a control strategy generated by a method as previouslydescribed with reference to at least FIGS. 1 to 6C and 8.

TABLE 1 Parameter Value Unit Filter inducance 0.7 mH Filter capacitance(delta) 8.3 μF Damping resistor 15 Ω Load inductance 3.75 mH Loadresistance 10 Ω Switching frequency 12.5 kHz Supply Voltage(rms) 90 V

Table 1 illustrates exemplary parameters for the system underdoingexperimentation. The filter inductance and capacitance is for a filterwhich filters an AC source provided to a matrix converter (having aSupply Voltage) previously described (such as input filter 83 b). Theinput filter consists of a LC filter with a damping resistor (of dampingresistance) parallel to the inductor. The input filter may be requiredto attenuate switching frequency harmonics. The system has a load of aload inductance and load resistance. A switching frequency indicates aswitching frequency of the matrix converter.

Consider a scenario in which a load current of 5 A at 30 Hz is demandedfrom the system, which results in a three phase output currents asillustrated by a first diagram 111 of FIG. 11A. In particular, there isillustrated a voltage output associated with a first phase 111A, asecond phase 111B and a third phase 111C. FIG. 11A also illustrates asecond diagram 112 showing a matrix converter output line voltage 112and a third diagram illustrating a harmonic spectrum 113 (of one of thethree-phases).

The harmonic spectrum indicates harmonics at switching frequency (12.5kHz) and its multiples. This implies that a fixed switching frequency isadvantageously generated by proposed control strategy. The totalharmonic distortion (THD) of the controlled waveform is about 3.97%.

In order to test the transient behavior of the control strategy, a stepdemand in the magnitude (e.g. from 2 to 5 A) and frequency (e.g. from20-40 Hz) of the output current of the matrix converter may berequested. That is, the desired output current of the matrix convertermay be changed from a current with magnitude 2 A, frequency 20 Hz to acurrent with magnitude 5 A, frequency 40 Hz.

The resulting load current waveforms are illustrated in FIG. 11B andindicates the fast transient response achieved by this method.

In particular, FIG. 11B indicates the three phase load current 114 for astep in demand, which illustrates a fast response to a change in desiredoutput current. That is, the output current of the matrix deviceimmediately responds to the change in desired current.

FIG. 11B also illustrates a mathematical (e.g. alpha-beta)transformation result 115 of the three phase output current by thematrix converter, represented by a first 115A and second 115B line.Here, the first line 115A represents an instantaneous alpha-part of thetransformation result, and the second line 1158 represents aninstantaneous beta-part of the transformation result.

Due to the low total harmonic distortion, it may be understood that adescribed method provides a quick and responsive control strategy forthe matrix converter with low harmonic distortion.

Embodiments described herein relate to a method of generating a controlstrategy for a multi-phase output matrix converter operably in aplurality of switching states. Such a method comprises obtaining adesired multi-phase output current of the matrix converter, obtainingpredicted multi-phase output currents of the matrix converter operatingin particular switching states, and determining a control strategy basedon the desired multi-phase output current and the predicted multi-phaseoutput currents.

In particular embodiments, mathematical transformations of the desiredoutput current and the predicted output currents are used to identify atleast three switching states for use in a control strategy.

Other variations to the disclosed embodiments can be understood andeffected by those skilled in the art in practicing the claimedinvention, from a study of the drawings, the disclosure, and theappended claims. Other bidirectional switches than explicitly hereindisclosed will be known to the person skilled in the art, for example, adiode bridge bi-directional switch cell. In the claims, the word“comprising” does not exclude other elements or steps, and theindefinite article “a” or “an” does not exclude a plurality. The merefact that certain measures are recited in mutually different dependentclaims does not indicate that a combination of these measured cannot beused to advantage. Any reference signs in the claims should not beconstrued as limiting the scope.

1. A method of generating a control strategy for a multi-phase outputmatrix convertor, the matrix converter being operable in a plurality ofswitching states, the method comprising: obtaining a target outputtransformation result representing a mathematical transformation resultof a desired multi-phase output current of the matrix converter;identifying a plurality of switching states of the matrix converter;obtaining, for each switching state in the identified plurality ofswitching states, a predicted output transformation result representinga mathematical transformation result of a predicted output current forthe switching state; identifying from the plurality of switching statesat least three switching states, wherein, when mapped using a Cartesianco-ordinate system, a position of the target output transformationresult is contained by an area defined by the positions of the predictedoutput transformation results associated with the at least threeswitching states; and generating a control strategy for the matrixconverter based on the at least three switching states.
 2. The method ofclaim 1, wherein the obtaining, for each switching state in theidentified plurality of switching states, a predicted outputtransformation result comprises: obtaining, for each switching state, apredicted output transformation result from a simulated or mathematicalmodel of the matrix converter and a load of the matrix converter.
 3. Themethod of claim 1, wherein the obtaining, for each switching state inthe identified plurality of switching states, a predicted outputtransformation result comprises: predicting, using a simulated ormathematical model of the matrix converter and a load of the matrixconverter, an output current of the matrix converter associated witheach switching state in the identified plurality of switching states;and performing a mathematical transformation on the predicted outputcurrent associated with each switching state to thereby obtain apredicted output transformation result for each switching state in theidentified plurality of switching states.
 4. The method of claim 1,wherein the identifying the at least three switching states comprises:obtaining, for each switching state in the identified plurality ofswitching state, a predicted output transformation result errorrepresenting a predicted error between the predicted outputtransformation result associated with the switching state and the targetoutput transformation result; and identifying at least three switchingstates, wherein, when mapped using a Cartesian co-ordinate system, aposition of the origin is contained by an area defined by the positionsof the predicted output transformation result errors associated with theat least three switching states.
 5. The method of claim 1, wherein theidentifying a plurality of switching states comprises: obtaining atarget input transformation result representing a mathematicaltransformation result of a desired input current of the matrixconverter; obtaining, for each possible switching state of the matrixconvertor, an input transformation result representing a mathematicaltransformation result of a current input of the matrix converterassociated with the possible switching state; identifying a plurality ofinput transformation results that are, when mapped using a Cartesianco-ordinate system, proximate to the position of the target inputtransformation result; and identifying the plurality of switching statesassociated with the identified plurality of input transformationresults.
 6. The method of claim 1, wherein the identifying a pluralityof switching states comprises: obtaining, for each possible switchingstate of the matrix convertor, a second output transformation resultrepresenting a mathematical transformation result of a voltage output ofthe matrix converter associated with the possible switching state; andidentifying the at least three switching states based on a magnitude ofthe second output transformation results.
 7. The method of claim 1,wherein the identifying a plurality of switching states based on amagnitude of the second output transformation results comprisesidentifying the plurality of switching states associated with the secondoutput transformation results of the largest magnitude.
 8. The method ofclaim 1, wherein the identifying the at least three switching statescomprises: identifying a first switching state for which a voltagedifference between all output terminals of the matrix converteroperating according to the first switching state is substantially zero;identifying a second switching state for which a voltage differencebetween at least two output terminals of the matrix converter operatingaccording to the second switching state is non-zero; and identifying athird switching state for which a voltage difference between at leasttwo output terminals of the matrix converter operating according to thethird switching state is non-zero.
 9. The method of claim 1, whereingenerating the control strategy comprises: calculating a duty cycle forthe at least three switching states based on the target outputtransformation result; and generating the control strategy for thematrix converter based on the calculated duty cycles.
 10. The method ofclaim 1, wherein the mathematical transformation is an alpha-betatransformation, such that the target output transformation resultrepresents an alpha-beta transformation result of a desired multi-phaseoutput current of the matrix converter and each predicted outputtransformation result represents an alpha-beta transformation result ofa predicted output current for a respective switching state.
 11. Anon-transitory computer-readable medium comprising instructions that,when executed by one or more processors and computer memory, cause theone or more processors to perform operations comprising: obtaining atarget output transformation result representing a mathematicaltransformation result of a desired multi-phase output current of thematrix converter; identifying a plurality of switching states of thematrix converter; obtaining, for each switching state in the identifiedplurality of switching states, a predicted output transformation resultrepresenting a mathematical transformation result of a predicted outputcurrent for the switching state; and identifying from the plurality ofswitching states at least three switching states, wherein, when mappedusing a Cartesian co-ordinate system, a position of the target outputtransformation result is contained by an area defined by the positionsof the predicted output transformation results associated with the atleast three switching states; and generating a control strategy for thematrix converter based on the at least three switching states.
 12. Acontrol strategy generator for a multi-phase output matrix convertor,the matrix converter being operable in a plurality of switching states,each switching state being associated with a respective switching state,the control strategy generator comprising a processor which is adaptedto: obtain a target output transformation result representing amathematical transformation result of a desired multi-phase outputcurrent of the matrix converter; identify a plurality of switchingstates of the matrix converter; obtain, for each switching state in theidentified plurality of switching states, a predicted outputtransformation result representing a mathematical transformation resultof a predicted output current for the switching state; identify from theplurality of switching states at least three switching states, wherein,when mapped using a Cartesian co-ordinate system, a position of thetarget output transformation result is contained by an area defined bythe positions of the predicted output transformation results associatedwith the at least three switching states; and generate a controlstrategy for the matrix converter based on the at least three switchingstates.
 13. The control strategy generator of claim 12, wherein theprocessor is adapted to obtain, for each switching state, a predictedoutput transformation result from a simulated or mathematical model ofthe matrix converter and a load of the matrix converter.
 14. The controlstrategy generator of any of claim 12, wherein the processor is adaptedto: predict, using a simulated or mathematical model of the matrixconverter and a load of the matrix converter, an output current of thematrix converter associated with each switching state in the identifiedplurality of switching states; and perform a mathematical transformationon the predicted output current associated with each switching state tothereby obtain a predicted output transformation result for eachswitching state in the identified plurality of switching states.
 15. Thecontrol strategy generator of any of claim 12, wherein the processor isadapted to: obtain, for each switching state in the identified pluralityof switching state, a predicted output transformation result errorrepresenting a predicted error between the predicted outputtransformation result associated with the switching state and the targetoutput transformation result; and identify at least three switchingstates, wherein, when mapped using a Cartesian co-ordinate system, aposition of the origin is contained by an area defined by the positionsof the predicted output transformation result errors associated with theat least three switching states.
 16. The non-transitorycomputer-readable medium of claim 11, wherein the obtaining, for eachswitching state in the identified plurality of switching states, apredicted output transformation result comprises: obtaining, for eachswitching state, a predicted output transformation result from asimulated or mathematical model of the matrix converter and a load ofthe matrix converter.
 17. The non-transitory computer-readable medium ofclaim 11, wherein the obtaining, for each switching state in theidentified plurality of switching states, a predicted outputtransformation result comprises: predicting, using a simulated ormathematical model of the matrix converter and a load of the matrixconverter, an output current of the matrix converter associated witheach switching state in the identified plurality of switching states;and performing a mathematical transformation on the predicted outputcurrent associated with each switching state to thereby obtain apredicted output transformation result for each switching state in theidentified plurality of switching states.
 18. The non-transitorycomputer-readable medium of claim 11, wherein the identifying the atleast three switching states comprises: obtaining, for each switchingstate in the identified plurality of switching state, a predicted outputtransformation result error representing a predicted error between thepredicted output transformation result associated with the switchingstate and the target output transformation result; and identifying atleast three switching states, wherein, when mapped using a Cartesianco-ordinate system, a position of the origin is contained by an areadefined by the positions of the predicted output transformation resulterrors associated with the at least three switching states.
 19. Thenon-transitory computer-readable medium of claim 11, wherein theidentifying a plurality of switching states comprises: obtaining atarget input transformation result representing a mathematicaltransformation result of a desired input current of the matrixconverter; obtaining, for each possible switching state of the matrixconvertor, an input transformation result representing a mathematicaltransformation result of a current input of the matrix converterassociated with the possible switching state; identifying a plurality ofinput transformation results that are, when mapped using a Cartesianco-ordinate system, proximate to the position of the target inputtransformation result; and identifying the plurality of switching statesassociated with the identified plurality of input transformationresults.
 20. The non-transitory computer-readable medium of claim 11,wherein the identifying a plurality of switching states comprises:obtaining, for each possible switching state of the matrix convertor, asecond output transformation result representing a mathematicaltransformation result of a voltage output of the matrix converterassociated with the possible switching state; and identifying the atleast three switching states based on a magnitude of the second outputtransformation results.